Micro- and nano-mechanical resonant devices (or “MR devices”) have found a wide variety of applications, including resonant accelerometers, gyroscopes, energy scavengers, oscillators, electrical filters, infrared sensors, and physical instruments. For all these applications, two figures of merit for the design of these devices are the resonant frequency and the mechanical quality factor (“Q factor” or “Q”). For the purposes herein, reference to “mechanical resonant (MR) device” includes micro- and nano-mechanical resonance devices.
The resonant frequency provides information about the resonance characteristics of the device, while the Q factor is a measurement of energy dissipation of the device during its vibrations. Q may be considered to be a comparison of the frequency of vibration to the rate of energy dissipation, or the stored maximum vibration energy per vibration cycle to the energy dissipation per cycle. There are a variety of energy dissipation mechanisms, such as support loss, surface loss, thermoelastic damping, etc. If Q is high, then the dissipation rate of energy is low, while a lower Q indicates a relatively greater dissipation of energy per vibration cycle.
Thermo-elastic damping imposes the upper limit of the achievable Q in a resonator. The mechanism of thermo-elastic damping is that a change of temperature of a device may cause thermo-elastic deformation, and conversely, a mechanical deformation may cause a change of temperature. As a device vibrates or oscillates, the coupling between heat conduction and strain rate will induce a form of irreversible heat generation, which generation is referred to as “thermo-elastic damping” or TED. Thus, QTED is the quality factor attributable to thermo-elastic damping.
Various engineering software applications or tools are available to assist the design of micro- and nano-mechanical resonant devices. Such tools are relatively comprehensive and assist in simulating a concept, developing a prototype, and testing; these tools may be used for simulation of physical dynamics, thermal issues, electrical, and other domains.
Although the prediction of the resonant frequency may be determined by using such finite element modeling (FEM) software, an effective and easy-to-use tool for prediction of the Q is not available. In most cases, the Q will not be known until experimental measurement is implemented, which is costly and time-consuming. Therefore, a quantitative evaluation or predictive system for determining the Q is of significant importance for developing micro- and nano-mechanical resonators.